Quantum approaches to music cognition

Journal of Mathematical Psychology

Volumn 91, Issue , 2019, Pages 38-50

  beim Graben, Peter ^a   Blutner, Reinhard ^b  

^a BRANDENBURG UNIVERSITY OF TECHNOLOGY   (Germany)

^b UNIVERSITY OF AMSTERDAM   (Netherlands)

Author keywords

Music psychology; Quantum cognition; Tonal attraction; Tonal space

Indexed keywords

EID: 85063110584     PISSN: 00222496     EISSN: 10960880     Source Type: Journal    
DOI: 10.1016/j.jmp.2019.03.002     Document Type: Article

References (49)

1. Balzano, G.J., The group-theoretic description of 12-fold and microtonal pitch systems. Computer Music Journal 4:4 (1980), 66–84.
2. Blutner, R., Modelling tonal attraction: tonal hierarchies, interval cycles, and quantum probabilities. Soft Computing, 2015, 1–19.
3. Blutner, R., beim Graben, P., Quantum cognition and bounded rationality. Synthese 193 (2016), 3239–3291.
4. Busemeyer, J.R., Bruza, P.D., (eds.) Quantum models of cognition and decision, 2012, Cambridge University Press.
5. Curtis, M.E., Bharucha, J.J., Memory and musical expectation for tones in cultural context. Music Perception: An Interdisciplinary Journal 26:4 (2009), 365–375.
6. Durrant, S., Miranda, E.R., Hardoon, D., Shawe-Taylor, J., Brechmann, A., Scheich, H., Neural correlates of tonality in music. Proceedings of the NIPS conference workshop on music, brain & cognition, 2007.
7. beim Graben, P., Blutner, R., Toward a gauge theory of musical forces. de Barros, J.A., Coecke, B., Pothos, E., (eds.) Quantum interaction. 10th international conference (QI 2016) LNCS, vol. 10106, 2017, Springer, Cham, 99–111.
8. Granot, R.Y., Hai, A., Electrophysiological evidence for a two-stage process underlying single chord priming. NeuroReport, 20(9), 2009.
9. Janata, P., Navigating tonal space. Selfridge-Field, E., Hewlett, W.B., (eds.) Tonal theory for the digital age Computing in musicology, vol. 15, 2007, MIT Press, Cambridge (MA), 39–50.
10. Janata, P., Birk, J.L., Horn, J.D.V., Leman, M., Tillmann, B., Bharucha, J.J., The cortical topography of tonal structures underlying western music. Science 298:5601 (2002), 2167–2170.
11. Johnson-Laird, P.N., Kang, O.E., Leong, Y.C., On musical dissonance. Music Perception: An Interdisciplinary Journal 30:1 (2012), 19–35.
12. Koelsch, S., Gunter, T.C., von Cramon, D.Y., Zysset, S., Lohmann, G., Friederici, A.D., Bach speaks: a cortical “language-network” serves the processing of music. NeuroImage 17:2 (2002), 956–966.
13. Köhler, W., The task of gestalt psychology. 1969, Princeton University Press, New Jersey.
14. Krumhansl, C.L., The psychological representation of musical pitch in a tonal context. Cognitive Psychology 11:3 (1979), 346–374.
15. Krumhansl, C.L., Cuddy, L.L., A theory of tonal hierarchies in music. Jones, M.R., Fay, R.R., Popper, A.N., (eds.) Music perception Springer handbook of auditory research, 2010, Springer, New York, 51–87.
16. Krumhansl, C.L., Kessler, E.J., Tracing the dynamic changes in perceived tonal organization in a spatial representation of musical keys. Psychological Review 89:4 (1982), 334–368.
17. Krumhansl, C.L., Shepard, R.N., Quantification of the hierarchy of tonal functions within a diatonic context. Journal of Experimental Psychology: Human Perception and Performance, 5(4), 1979, 579.
18. Krumhansl, C.L., Toivanen, P., Eerola, T., Toiviainen, P., Järvinen, T., Louhivuori, J., Cross-cultural music cognition: Cognitive methodology applied to North Sami yoiks. Cognition 76:1 (2000), 13–58.
19. Larson, S., Musical forces: Motion, metaphor, and meaning in music. 2012, Indiana University Press.
20. Lerdahl, F., Tonal pitch space. Music Perception: An Interdisciplinary Journal 5 (1988), 315–350.
21. Lerdahl, F., Calculating tonal tension. Music Perception: An Interdisciplinary Journal 13:3 (1996), 319–363.
22. Lerdahl, F., Concepts and representations of musical hierarchies. Music Perception: An Interdisciplinary Journal 33:1 (2015), 83–95.
23. Lerdahl, F., Jackendoff, R., A generative theory of tonal music. 1983, MIT Press, Cambridge (MA).
24. Limb, C.J., Structural and functional neural correlates of music perception. The Anatomical Record Part A: Discoveries in Molecular, Cellular, and Evolutionary Biology 288A:4 (2006), 435–446.
25. Mannone, M., Knots, music, and DNA. Journal of Creative Music Systems, 2(2), 2018.
26. Mannone, M., & Compagno, G. (2013). Characterization of the degree of musical non-Markovianity. arXiv:1306.0229 [physics.data-an].
27. Mannone, M., Mazzola, G., Hypergestures in complex time: creative performance between symbolic and physical reality. Collins, T., Meredith, D., Volk, A., (eds.) Proceedings of the 5th international conference on mathematics and computation in music (MCM 2015), 2015, Springer, Cham, 137–148.
28. Mazzola, G., Geometrie der töne. 1990, Birkhäuser, Basel.
29. Mazzola, G., The topos of music: Geometric logic of concepts, theory, and performance. 2002, Birkhäuser, Basel.
30. Mazzola, G., Mannone, M., Pang, Y., Cool math for hot music Computational music science, 2016, Springer, Cham.
31. Milne, A.J., Laney, R., Sharp, D.B., A spectral pitch class model of the probe tone data and scalic tonality. Music Perception: An Interdisciplinary Journal 32:4 (2015), 364–393.
32. Milne, A.J., Sethares, W.A., Laney, R., Sharp, D.B., Modelling the similarity of pitch collections with expectation tensors. Journal of Mathematics and Music 5:1 (2011), 1–20.
33. Narmour, E., The analysis and cognition of melodic complexity: The implication-realization model. 1992, University of Chicago Press, Chicago (IL).
34. Parncutt, R., Harmony: A psychoacoustical approach. 1989, Springer, Berlin.
35. Parncutt, R., The tonic as triad: Key profiles as pitch salience profiles of tonic triads. Music Perception: An Interdisciplinary Journal 28:4 (2011), 333–366.
36. Pothos, E.M., Busemeyer, J.R., Can quantum probability provide a new direction for cognitive modeling?. Behavioral and Brain Sciences 36 (2013), 255–274.
37. Pothos, E.M., Busemeyer, J.R., Trueblood, J.S., A quantum geometric model of similarity. Psychological Review 120:3 (2013), 679–696.
38. Pothos, E.M., Trueblood, J.S., Structured representations in a quantum probability model of similarity. Journal of Mathematical Psychology 64–65 (2015), 35–43.
39. Purwins, H., Blankertz, B., Obermayer, K., Toroidal models in tonal theory and pitch-class analysis. Selfridge-Field, E., Hewlett, W.B., (eds.) Tonal theory for the digital age Computing in musicology, vol. 15, 2007, MIT Press, Cambridge (MA), 73–98.
40. Quinn, I., On Woolhouse's interval-cycle proximity hypothesis. Music Theory Spectrum 32 (2010), 172–179.
41. Schönberg, A., Theory of harmony. 1978, University of California Press, Berkeley (CA).
42. Stolzenburg, F., Harmony perception by periodicity detection. Journal of Mathematics and Music 9:3 (2015), 215–238.
43. Temperley, D., Music and probability. 2007, MIT Press, Cambridge (MA).
44. Temperley, D., A probabilistic model of melody perception. Cognitive Science 32:2 (2008), 418–444.
45. v. Helmholtz, H., On the sensations of tones. 1877, Dover New York (NY) Translated by A. J. Ellis.
46. Vaquero, L., Hartmann, K., Ripollés, P., Rojo, N., Sierpowska, J., François, C., et al. Structural neuroplasticity in expert pianists depends on the age of musical training onset. NeuroImage 126:Supplement C (2016), 106–119.
47. Woolhouse, M., Modelling tonal attraction between adjacent musical elements. Journal of New Music Research 38:4 (2009), 357–379.
48. Woolhouse, M., Wagner in the round: using interval cycles to model chromatic harmony. Cambouropoulos, E., Tsougras, C., Mavromatis, P., Pastiadis, K., (eds.) Proceedings of the 12th international conference on music perception and cognition and the 8th triennial conference of the european society for the cognitive sciences of music, 2012, 1142–1145.
49. Woolhouse, M., Cross, I., Using interval cycles to model Krumhansl's tonal hierarchies. Music Theory Spectrum 32:1 (2010), 60–78.